Given two arrays A[] and B[] as position vector of two points in n-dimensional space along with an integer p, the task is to calculate Minkowski Distance between these two points.
The Minkowski distance is a generalization of other distance measures, such as Euclidean and Manhattan distances, and is defined as:
where A and B are vectors representing points in the multidimensional space, n is the number of dimensions, and p is a positive constant known as the order parameter.
Examples:
Input: A[] = {1,2,3,4}, B[] = {5,6,7,8}, P = 3
Output: 6.340Input: A = {1,2,3,4}, B[] = {5,6,7,8} P = 2
Output: 8
Approach:
Traverse using loop and calculate X as {(A1 – B1)P + (A2 – B2)P . . . (AN – BN)P}. Then calculate Minkowski Distance as X(1/P)
Step-by-step approach:
- Create a variable let say X.
-
Run a loop and follow below mentioned steps under the scope of loop:
- X += Power ((Ai – Bi), P)
- Calculate Z as (1/P)
- Return Power(X, Z)
Below is the implementation of the above approach:
// CPP code to implement the approach #include <bits/stdc++.h> using namespace std;
// Function to calculate Minkowski double minkowski( const vector< double >& A,
const vector< double >& B, double P)
{ // Variable to store value of X
double X = 0.0;
// Loop to calculate value of X
for ( size_t i = 0; i < A.size(); ++i) {
X += pow ( abs (A[i] - B[i]), P);
}
// Calculating Z as (1/P)
double Z = 1.0 / P;
// Returning X^(1/P) as X^Z
return pow (X, Z);
} int main()
{ // Input vectors
vector< double > A = { 1, 2, 3, 4 };
vector< double > B = { 5, 6, 7, 8 };
double P = 2.0;
//Function_ call
cout << minkowski(A, B, P) << endl;
return 0;
} |
import java.util.ArrayList;
import java.util.List;
public class MinkowskiDistance {
// Function to calculate Minkowski
private static double
minkowski(List<Double> A, List<Double> B, double P)
{
// Variable to store value of X
double X = 0.0 ;
// Loop to calculate value of X
for ( int i = 0 ; i < A.size(); ++i) {
X += Math.pow(Math.abs(A.get(i) - B.get(i)), P);
}
// Calculating Z as (1/P)
double Z = 1.0 / P;
// Returning X^(1/P) as X^Z
return Math.pow(X, Z);
}
public static void main(String[] args)
{
// Input vectors
List<Double> A = List.of( 1.0 , 2.0 , 3.0 , 4.0 );
List<Double> B = List.of( 5.0 , 6.0 , 7.0 , 8.0 );
double P = 2.0 ;
// Function call
System.out.println(minkowski(A, B, P));
}
} |
import math
# Function to calculate Minkowski def minkowski(A, B, P):
# Variable to store value of X
X = 0.0
# Loop to calculate value of X
for i in range ( len (A)):
X + = abs (A[i] - B[i]) * * P
# Calculating Z as (1/P)
Z = 1.0 / P
# Returning X^(1/P) as X^Z
return X * * Z
if __name__ = = "__main__" :
# Input lists
A = [ 1 , 2 , 3 , 4 ]
B = [ 5 , 6 , 7 , 8 ]
P = 2.0
# Function call
print (minkowski(A, B, P))
# This code is contributed by rambabuguphka |
using System;
using System.Collections.Generic;
public class Program
{ // Function to calculate Minkowski distance
static double Minkowski(List< double > A, List< double > B, double P)
{
// Variable to store value of X
double X = 0.0;
// Loop to calculate value of X
for ( int i = 0; i < A.Count; ++i)
{
X += Math.Pow(Math.Abs(A[i] - B[i]), P);
}
// Calculating Z as (1/P)
double Z = 1.0 / P;
// Returning X^(1/P) as X^Z
return Math.Pow(X, Z);
}
public static void Main()
{
// Input lists
List< double > A = new List< double > { 1, 2, 3, 4 };
List< double > B = new List< double > { 5, 6, 7, 8 };
double P = 2.0;
// Function call
Console.WriteLine(Minkowski(A, B, P));
}
} // This code is contributed by akshitaguprzj3 |
// Function to calculate Minkowski function minkowski(A, B, P) {
// Variable to store value of X
let X = 0.0;
// Loop to calculate value of X
for (let i = 0; i < A.length; ++i) {
X += Math.pow(Math.abs(A[i] - B[i]), P);
}
// Calculating Z as (1/P)
let Z = 1.0 / P;
// Returning X^(1/P) as X^Z
return Math.pow(X, Z);
} // Input arrays let A = [1, 2, 3, 4]; let B = [5, 6, 7, 8]; let P = 2.0; // Function call console.log(minkowski(A, B, P)); |
Output
8
Time Complexity: O(n * log2(p))
Auxiliary Space: O(1)
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